Can the opponent's Vi Peacekeeper use her ambush to react to the ability of my Mindsplitter and put it onto a battlefield where the opponent has a unit?

No, your opponent cannot use Vi, Peacekeeper's Ambush to "react" to the triggered ability of Mindsplitter in the way you are describing. Here is the breakdown of why this interaction functions this way:

1. Timing of the Ambush

Ambush allows a unit to be played as a [Reaction] to a battlefield where the controller has a unit. Because it is a [Reaction], it can be played while the game state is Closed (for example, while an ability is on the chain).

However, playing a unit (even via Ambush) simply places that unit onto the battlefield. It does not allow you to "react to an ability" in the sense of putting the unit into play instead of that ability or in response to the ability's effect. The unit is simply played to the battlefield as its own independent game action, which finalizes immediately (RiftJudge FAQ #9978).

2. The Chain

When you play Mindsplitter, the following happens:

1. Mindsplitter is played to a battlefield. It enters play immediately.
2. Mindsplitter's "When you play me" ability triggers and is placed on the chain.
3. Because an item (the ability) is now on the chain, the game state is Closed.
4. Your opponent now has the opportunity to play [Reaction] speed cards or abilities.
5. If they have Vi, Peacekeeper and control a unit at a battlefield, they can use Ambush to play her to that battlefield as a [Reaction] to your Mindsplitter ability.

3. The Result

While your opponent can play Vi, Peacekeeper as a reaction to your Mindsplitter ability, doing so does not stop or replace the Mindsplitter ability.

• Vi, Peacekeeper will enter the battlefield.
• The chain still contains your Mindsplitter ability.
• Once the chain resolves (or if both players pass priority on the chain), your Mindsplitter ability will still execute, forcing your opponent to reveal their hand and discard a card.

In summary, playing Vi, Peacekeeper via Ambush is a valid response to your ability being on the chain, but it does not prevent your ability from resolving.